MATHEMATICS Simple Angle Facts Aims of the Lesson • By the end of the lesson you should… • know the terms complementary and.
Download ReportTranscript MATHEMATICS Simple Angle Facts Aims of the Lesson • By the end of the lesson you should… • know the terms complementary and.
Slide 1
MATHEMATICS
Simple Angle Facts
Slide 2
Aims of the Lesson
• By the end of the lesson you should…
• know the terms complementary and supplementary
(in the context of angles) as well as vertically opposite
• be able to find missing angles…
• Within right angles
• On straight lines
• Around a point
• Inside triangles
• Inside quadrilaterals
Slide 3
Complementary Angles
• Together, complementary angles form a
right angle.
• Therefore they add up to 90°
Workings (example 1):
x + 47 = 90
43 + 47 = 90
so x = 43
47
x
Workings (example 2):
x + 47 = 90
90 – 47 = 43
so x = 43
Slide 4
• In the first worked example you are asking what value added to
47 gives a total of 90.
• In the second worked example you are saying if I take the 47
off the 90, x will be the value that is left over.
• (This is the recommended method!)
• You can choose either of these methods or one of your that
works, and when undertaking additions and subtractions you
can of course use the column method.
• Save and complete the worksheet: AngleComp-S1.xlsx
Slide 5
Supplementary Angles
• Together, supplementary angles form a
straight angle or a straight line.
• Therefore they add up to 180°
Workings (example 1):
x + 121 = 180
59 + 121 = 180 so x = 59
121
x
Workings (example 2):
x + 121 = 180
180 – 121 = 59
so x = 59
Slide 6
• In the first worked example you are asking what value
added to 121 gives a total of 180.
• In the second worked example you are saying if I take the
121 away from 180, x will be the value that is left over.
• (This is the recommended method!)
• You can choose either of these methods or one of your
that works, and when undertaking additions and
subtractions you can of course use the column method.
Slide 7
Angles around a point
• Together, angles round a point form a
complete circle.
• Therefore they add up to 360°
Workings (example 1):
x + (133 + 168) = 360
301
= 360
59 +
133 x
168
Workings (example 2):
x + (133 + 168) = 360
x +
301
= 360
360 – 301 = 59
so x = 59
so x = 59
Slide 8
• In the first worked example you are asking what value added to
133 and 168 (which together make 301) gives a total of 360.
• In the second worked example you are adding together all the
known angles (133 and 168) then saying if I take the 301 off
the 360, x will be the value that is left over.
• (This is the recommended method!)
• You can choose either of these methods or one of your that
works, and when undertaking additions and subtractions you
can of course use the column method.
• Save and complete the worksheet: AnglesSLP-S1.xlsx
Slide 9
Angles in a Triangle
• Together, the three angles in any triangle always
add up to 180°
• Look out for special triangles that have lines of
symmetry or contain right angles.
63°
63°
x
Before starting to work out ‘x’
you should note that 2 lines
are of equal
length.
Worked
example:
x + (63 + 63) = 180
This
x + means
126 that=there
180 is a
line
180of–symmetry
126 = 54 here…
so x = 54
This also means that the
angle left blank is also 63…
Slide 10
• In this worked example you are adding the two angles you
know (63 and 63) together. By taking their total (126) away
from 180, you are finding what is left over, which is the value of
the last angle, x.
• The example shows the addition and subtraction written in
lines, but you could use column methods of you wish.
• Work through the MyMaths lesson and then its online
homework called: Shape > Angles > Angle Sums
• Lesson: http://app.mymaths.co.uk/256-resource/angle-sums
• HW: http://app.mymaths.co.uk/256-homework/angle-sums
Slide 11
Angles in a Quadrilateral
• Together, the four angles in any 4-sided shape
always add up to 360°
• Look out for special properties or right angles.
97°
x
41°
97°
You are told that although no
properties are marked on it, this
shape isexample:
a kite.
Worked
x + (97 + 97 + 41) = 360
You
know =
it has
x +therefore
235
360 a line
of360
symmetry
– 235 =here…
125
so x = 125
..and thus the angle left blank is
actually 97°.
Slide 12
• In this worked example you are adding the three angles
you know (97, 97 and 41) together. By taking their total
(235) away from 360, you are finding what is left over,
which is the value of the last angle, x.
• The example shows the addition and subtraction written in
a line, but you could use column methods of you wish.
• Save and complete the worksheet: AnglesTQ-S1.xlsx
Slide 13
Vertically Opposite Angles
• Whenever any two straight lines cross you get four
angles.
• These are two pairs of vertically opposite angles.
4
1
3
2
• Unless the two lines cross at right angles (i.e. are
perpendicular), then there will be two acute angles and
two obtuse angles.
• Vertically opposite angles are EQUAL to each other.
Slide 14
What next?
• Print out the notes called Angle3-Simple.docx and answer
the questions.
• Work through the MyMaths lesson called Angle
Reasoning found at:
http://app.mymaths.co.uk/257-resource/angle-reasoning
• Now move on to the Angle4 powerpoint
MATHEMATICS
Simple Angle Facts
Slide 2
Aims of the Lesson
• By the end of the lesson you should…
• know the terms complementary and supplementary
(in the context of angles) as well as vertically opposite
• be able to find missing angles…
• Within right angles
• On straight lines
• Around a point
• Inside triangles
• Inside quadrilaterals
Slide 3
Complementary Angles
• Together, complementary angles form a
right angle.
• Therefore they add up to 90°
Workings (example 1):
x + 47 = 90
43 + 47 = 90
so x = 43
47
x
Workings (example 2):
x + 47 = 90
90 – 47 = 43
so x = 43
Slide 4
• In the first worked example you are asking what value added to
47 gives a total of 90.
• In the second worked example you are saying if I take the 47
off the 90, x will be the value that is left over.
• (This is the recommended method!)
• You can choose either of these methods or one of your that
works, and when undertaking additions and subtractions you
can of course use the column method.
• Save and complete the worksheet: AngleComp-S1.xlsx
Slide 5
Supplementary Angles
• Together, supplementary angles form a
straight angle or a straight line.
• Therefore they add up to 180°
Workings (example 1):
x + 121 = 180
59 + 121 = 180 so x = 59
121
x
Workings (example 2):
x + 121 = 180
180 – 121 = 59
so x = 59
Slide 6
• In the first worked example you are asking what value
added to 121 gives a total of 180.
• In the second worked example you are saying if I take the
121 away from 180, x will be the value that is left over.
• (This is the recommended method!)
• You can choose either of these methods or one of your
that works, and when undertaking additions and
subtractions you can of course use the column method.
Slide 7
Angles around a point
• Together, angles round a point form a
complete circle.
• Therefore they add up to 360°
Workings (example 1):
x + (133 + 168) = 360
301
= 360
59 +
133 x
168
Workings (example 2):
x + (133 + 168) = 360
x +
301
= 360
360 – 301 = 59
so x = 59
so x = 59
Slide 8
• In the first worked example you are asking what value added to
133 and 168 (which together make 301) gives a total of 360.
• In the second worked example you are adding together all the
known angles (133 and 168) then saying if I take the 301 off
the 360, x will be the value that is left over.
• (This is the recommended method!)
• You can choose either of these methods or one of your that
works, and when undertaking additions and subtractions you
can of course use the column method.
• Save and complete the worksheet: AnglesSLP-S1.xlsx
Slide 9
Angles in a Triangle
• Together, the three angles in any triangle always
add up to 180°
• Look out for special triangles that have lines of
symmetry or contain right angles.
63°
63°
x
Before starting to work out ‘x’
you should note that 2 lines
are of equal
length.
Worked
example:
x + (63 + 63) = 180
This
x + means
126 that=there
180 is a
line
180of–symmetry
126 = 54 here…
so x = 54
This also means that the
angle left blank is also 63…
Slide 10
• In this worked example you are adding the two angles you
know (63 and 63) together. By taking their total (126) away
from 180, you are finding what is left over, which is the value of
the last angle, x.
• The example shows the addition and subtraction written in
lines, but you could use column methods of you wish.
• Work through the MyMaths lesson and then its online
homework called: Shape > Angles > Angle Sums
• Lesson: http://app.mymaths.co.uk/256-resource/angle-sums
• HW: http://app.mymaths.co.uk/256-homework/angle-sums
Slide 11
Angles in a Quadrilateral
• Together, the four angles in any 4-sided shape
always add up to 360°
• Look out for special properties or right angles.
97°
x
41°
97°
You are told that although no
properties are marked on it, this
shape isexample:
a kite.
Worked
x + (97 + 97 + 41) = 360
You
know =
it has
x +therefore
235
360 a line
of360
symmetry
– 235 =here…
125
so x = 125
..and thus the angle left blank is
actually 97°.
Slide 12
• In this worked example you are adding the three angles
you know (97, 97 and 41) together. By taking their total
(235) away from 360, you are finding what is left over,
which is the value of the last angle, x.
• The example shows the addition and subtraction written in
a line, but you could use column methods of you wish.
• Save and complete the worksheet: AnglesTQ-S1.xlsx
Slide 13
Vertically Opposite Angles
• Whenever any two straight lines cross you get four
angles.
• These are two pairs of vertically opposite angles.
4
1
3
2
• Unless the two lines cross at right angles (i.e. are
perpendicular), then there will be two acute angles and
two obtuse angles.
• Vertically opposite angles are EQUAL to each other.
Slide 14
What next?
• Print out the notes called Angle3-Simple.docx and answer
the questions.
• Work through the MyMaths lesson called Angle
Reasoning found at:
http://app.mymaths.co.uk/257-resource/angle-reasoning
• Now move on to the Angle4 powerpoint